Average and Standard Deviation Calculator

How to use

1. Paste or type your numbers into the box above.
2. Separate values with commas, spaces, or line breaks (Excel column pastes work).
3. Click Calculate (or press Ctrl+Enter / ⌘+Enter).
4. Read count, sum, and mean, then compare sample vs population standard deviation and variance side by side.
5. If you see an error about n ≥ 2, add at least one more valid number for sample SD.

Formula

Let your numbers be x₁, x₂, …, xₙ with count n.

• Mean (average)
  Add every value and divide by how many you have:
  x̄ = (Σ xᵢ) / n
• Population standard deviation
  Use when your data is the full population. Divide the sum of squared differences from the mean by n:
  σ = √[ Σ (xᵢ − x̄)² / n ]
• Sample standard deviation
  Use when your data is a sample from a larger population. Divide by n − 1 (Bessel's correction):
  s = √[ Σ (xᵢ − x̄)² / (n − 1) ]

Variance is the square of the corresponding standard deviation (population variance uses ÷ n; sample variance uses ÷ (n − 1)).

Worked example

Dataset: 2, 4, 4, 4, 5, 5, 7, 9

• n = 8
• Sum = 40
• Mean = 40 ÷ 8 = 5
• Squared deviations from 5 sum to 32
• Population variance = 32 ÷ 8 = 4 → population SD = √4 = 2
• Sample variance = 32 ÷ 7 ≈ 4.571 → sample SD ≈ 2.138

Load the example in the calculator above and click Calculate to confirm these figures.

FAQ

Sample vs population — which should I use?

Use population SD when the numbers are the entire set you care about. Use sample SD when they are a sample used to estimate the spread of a larger population; that formula divides by n − 1 so the estimate is less biased.

Can I paste from Excel?

Yes. Copy a column or row from Excel or Google Sheets and paste it into the box. New lines and tabs are treated as separators, same as commas and spaces.

What about empty values?

Empty tokens (extra commas, blank lines, or stray spaces) are ignored. Only tokens that look like valid numbers are counted.

What if all values are identical?

The mean equals that value, and both sample and population standard deviation (and variance) are 0 — there is no spread in the data.